Limit rational function without L'H

[whatlifeforme]

Homework Statement

evaluate.

Homework Equations

$lim_{x->0+} \frac{\sqrt{x}}{\sqrt{sinx}}$

The Attempt at a Solution

i've tried l'hopital's and it is just endless cycle.

 

[Dick]

It's the same as sqrt(x/sin(x)). You know the limit of x/sin(x), right?

 

[Mark44]

Homework Statement

evaluate.

Homework Equations

$lim_{x->0+} \frac{\sqrt{x}}{\sqrt{sinx}}$

The Attempt at a Solution

i've tried l'hopital's and it is just endless cycle.

Sometimes, L'Hopital's Rule is not the way to go. Under the right conditions, you can switch the order of the limit operation and the function in the limit.
$\lim f(g(x)) = f(\lim g(x))$

Also, as long as all quantities are positive,
$$ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$

 

[whatlifeforme]

yes, but it is of the form 0/0.

 

[Dick]

yes, but it is of the form 0/0.

That doesn't mean you HAVE to use l'Hopital. You know the limit of x/sin(x), use l'Hopital on that. Then take the square root. Use that the square root is continuous for positive arguments.